YES(?,O(n^1)) We are left with following problem, upon which TcT provides the certificate YES(?,O(n^1)). Strict Trs: { a__zeros() -> cons(0(), zeros()) , a__zeros() -> zeros() , a__tail(X) -> tail(X) , a__tail(cons(X, XS)) -> mark(XS) , mark(cons(X1, X2)) -> cons(mark(X1), X2) , mark(0()) -> 0() , mark(zeros()) -> a__zeros() , mark(tail(X)) -> a__tail(mark(X)) } Obligation: innermost runtime complexity Answer: YES(?,O(n^1)) The problem is match-bounded by 4. The enriched problem is compatible with the following automaton. { a__zeros_0() -> 1 , a__zeros_1() -> 1 , a__zeros_2() -> 1 , a__zeros_3() -> 1 , cons_0(2, 2) -> 2 , cons_1(1, 2) -> 1 , cons_1(3, 4) -> 1 , cons_2(5, 6) -> 1 , cons_3(7, 8) -> 1 , cons_4(9, 10) -> 1 , 0_0() -> 2 , 0_1() -> 1 , 0_1() -> 3 , 0_2() -> 5 , 0_3() -> 7 , 0_4() -> 9 , zeros_0() -> 2 , zeros_1() -> 1 , zeros_1() -> 4 , zeros_2() -> 1 , zeros_2() -> 6 , zeros_3() -> 1 , zeros_3() -> 8 , zeros_4() -> 1 , zeros_4() -> 10 , a__tail_0(2) -> 1 , a__tail_1(1) -> 1 , mark_0(2) -> 1 , mark_1(2) -> 1 , mark_2(2) -> 1 , mark_2(4) -> 1 , mark_2(6) -> 1 , mark_2(8) -> 1 , mark_2(10) -> 1 , tail_0(2) -> 2 , tail_1(2) -> 1 , tail_2(1) -> 1 } Hurray, we answered YES(?,O(n^1))